Monday, July 18, 2011

A is for AVERAGES

Superficial people want to be it. Eccentric people think that it's the bane of all existence. Mathematicians think it's useful.
What am I talking about?
AVERAGES
What does it mean for something to be average?
Let's define it technically first, before we get into any moral discussions, shall we?
The average in statistics is typically referred to as the mean. The mean represents a set of data by showing the value that is most likely to minimize error. It's also known as the expected value, because it represents the value that is most expected if you are to add more data. You get it by adding up any data you have and dividing by the number of data you have. In this example, let's look at a bunch of test scores in a certain English class. They are the numbers you see down here. (85 92 73 84 87 64 96 90 88 71 94) Now add them up, and divide by however many numbers there are. Add them up and you get 924. Count and see there are 11 values. 924 divided by 11 is 84, which is the average score. Now, if a 12th person took the test, how well do you think she would do? Probably close to 84...that's why the average is also called the expected value.

When we say "expected value" we use the word "expected" very loosely. Here's another example. Let's say that we want to know what the average family looks like out of all your friends. You ask them how many brothers and sisters they have in their family, themselves included. Your 7 friends say that they have 2, 3, 5, 1, 0, 3, and 2 members of their generation in their respective families. To find the average, add them up to 16. Divide by 7, and you get that the average is about 2.3. What? How do you have 2.3 people in your family?

It looks like the average might not have a practical meaning of what exactly to expect, but that's why the mean is nothing more than a statistic. It represents a set of data, but the data is going to vary. It won't all be equal to the mean-- in fact, sometimes it's impossible for a value to be exactly average. In most cases, it's NOT POSSIBLE to be average. It may be possible to be close to average, but not exactly.

So what does it mean to be average? Most times, it's impossible to be average. And even when it is possible, it's very rare for something to be exactly equal to it.

But what does it mean for a person to be average? Is it possible? Are you one of the extremely rare people that is exactly average? Would you want to be average?